Q. A mass $m$ moves with a velocity $v\ $and collides inelastically with another identical mass. After collision the $1^{st}$ mass moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to the initial direction of motion. Find the speed of the second mass after collision.
A) $v$
B) $\sqrt{3\ v}$
C) $\frac{2}{\sqrt{3}}v$
D) $\frac{v}{\sqrt{3}}$
Explanation
(c) In x-direction
$mu_{1} + 0 = 0 + mv_{x}\ \ $
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Or $\ \ \ mv = mv_{x}$
Or $v_{x} = v$
In y-direction
$0 + 0 = m\left( \frac{v}{\sqrt{3}} \right) - mv_{y}$
Or $v_{y} = \frac{v}{\sqrt{3}}$
$\therefore$velocity of second mass after collision
$v^{''} = \sqrt{\left( \frac{v}{\sqrt{3}} \right)^{2} + v^{2}} = \sqrt{\frac{4}{3}v^{2}}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ v^{''} = \frac{2}{\sqrt{3}}v$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.